Ratios/Proportions in PS

[msw27]

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Hey guys,

My biggest problem on the PS section is the ratio/proportion questions. Does anyone have any tricks or tips? For example, when finding how an increase/decrease in one variable affects the equation. (I'm not talking in simple equations like F=ma). It takes me too long when questions ask about one variable, and that variable must be plugged into an additional equation to find out how some other variable in that equation is affected.

 

[DrMattOglesby]

do you mean in something like:

F = (Gm1m2)/r^2

and they ask you by what factor would the force be affected if you tripled the distance between the centers of the two masses?

you take that tripling effect and put a "3" before the "r^2" so that your equation looks like this:

F = (Gm1m2)/(3r^2)

3^2 = 9

so its like multiplying the force by a factor of 1/9 and hence the overall effect of tripling the distance(r) between the two masses brings the force to 1/9 its original value.

 

[msw27]

That's a great example of what I mean. However, the example that you provided is something I could have solved easily, but I'm speaking in terms of more complicated cases.

For Ex, take the problem you gave me. You found the affect of the increasing radius on the force. Now say you had to find the acceleration due to gravity on the same system. Easy right? Just divide one of the masses by the force that you calculated and you have the acceleration. Now say you have to take that calculated acceleration and increase it by, lets say, a factor of 4. I could still find the answer, but it would take me quite some time to do so.

So I suppose what I'm asking is, are these types of problems just something you have to get used to doing quickly? Because the rate I'm going kills my time. (I generally have to plug in arbitrary numbers to understand what's happening to the formula as well. Is that a bad habit to get into?)

 

[msw27]

Ps: Thanks for offering your help. I seem to never get any responses on my posts...haha

 

[tncekm]

The only way to really get better at proportions is to practice them.

Make your own up.

E.x. if an electron is traveling through a magnetic field (B) what effect on the diameter of the semicircle it makes will there be if the velocity is tripled (Where D₁ is the diameter and D₂is the diameter if tripled)?

mv²/r = qvB

r=mv²/qvB

D=2r

D=2mv²/qvB; Or, you could rewrite it as 4(½mv&#178😉/qvB and strangely enough this comes out to be that D = 4KE/F... I had no idea that was coming.

So,

D₁/D₂=v₁²/v₂² -->

D₁=D₂v₁²/v₂² =(1/9)*D₂, so increasing the velocity by three times increased the diameter by 9 times.

 

[DrMattOglesby]

tncekm,
how do you write super/sub-scripts????

 

[tncekm]

I have a mac and there is an easy to use character palette tool 😀

 

[iA-MD2013]

I have a mac and there is an easy to use character palette tool 😀

ohhh...I've always wondered that.